1 /*
2 * Single-precision SVE cos(x) function.
3 *
4 * Copyright (c) 2019-2024, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8 #include "sv_math.h"
9 #include "test_sig.h"
10 #include "test_defs.h"
11
12 static const struct data
13 {
14 float neg_pio2_1, neg_pio2_2, neg_pio2_3, inv_pio2, shift;
15 } data = {
16 /* Polynomial coefficients are hard-wired in FTMAD instructions. */
17 .neg_pio2_1 = -0x1.921fb6p+0f,
18 .neg_pio2_2 = 0x1.777a5cp-25f,
19 .neg_pio2_3 = 0x1.ee59dap-50f,
20 .inv_pio2 = 0x1.45f306p-1f,
21 /* Original shift used in AdvSIMD cosf,
22 plus a contribution to set the bit #0 of q
23 as expected by trigonometric instructions. */
24 .shift = 0x1.800002p+23f
25 };
26
27 #define RangeVal 0x49800000 /* asuint32(0x1p20f). */
28
29 static svfloat32_t NOINLINE
special_case(svfloat32_t x,svfloat32_t y,svbool_t oob)30 special_case (svfloat32_t x, svfloat32_t y, svbool_t oob)
31 {
32 return sv_call_f32 (cosf, x, y, oob);
33 }
34
35 /* A fast SVE implementation of cosf based on trigonometric
36 instructions (FTMAD, FTSSEL, FTSMUL).
37 Maximum measured error: 2.06 ULPs.
38 SV_NAME_F1 (cos)(0x1.dea2f2p+19) got 0x1.fffe7ap-6
39 want 0x1.fffe76p-6. */
SV_NAME_F1(cos)40 svfloat32_t SV_NAME_F1 (cos) (svfloat32_t x, const svbool_t pg)
41 {
42 const struct data *d = ptr_barrier (&data);
43
44 svfloat32_t r = svabs_x (pg, x);
45 svbool_t oob = svcmpge (pg, svreinterpret_u32 (r), RangeVal);
46
47 /* Load some constants in quad-word chunks to minimise memory access. */
48 svfloat32_t negpio2_and_invpio2 = svld1rq (svptrue_b32 (), &d->neg_pio2_1);
49
50 /* n = rint(|x|/(pi/2)). */
51 svfloat32_t q = svmla_lane (sv_f32 (d->shift), r, negpio2_and_invpio2, 3);
52 svfloat32_t n = svsub_x (pg, q, d->shift);
53
54 /* r = |x| - n*(pi/2) (range reduction into -pi/4 .. pi/4). */
55 r = svmla_lane (r, n, negpio2_and_invpio2, 0);
56 r = svmla_lane (r, n, negpio2_and_invpio2, 1);
57 r = svmla_lane (r, n, negpio2_and_invpio2, 2);
58
59 /* Final multiplicative factor: 1.0 or x depending on bit #0 of q. */
60 svfloat32_t f = svtssel (r, svreinterpret_u32 (q));
61
62 /* cos(r) poly approx. */
63 svfloat32_t r2 = svtsmul (r, svreinterpret_u32 (q));
64 svfloat32_t y = sv_f32 (0.0f);
65 y = svtmad (y, r2, 4);
66 y = svtmad (y, r2, 3);
67 y = svtmad (y, r2, 2);
68 y = svtmad (y, r2, 1);
69 y = svtmad (y, r2, 0);
70
71 if (unlikely (svptest_any (pg, oob)))
72 return special_case (x, svmul_x (svnot_z (pg, oob), f, y), oob);
73 /* Apply factor. */
74 return svmul_x (pg, f, y);
75 }
76
77 TEST_SIG (SV, F, 1, cos, -3.1, 3.1)
78 TEST_ULP (SV_NAME_F1 (cos), 1.57)
79 TEST_DISABLE_FENV (SV_NAME_F1 (cos))
80 TEST_INTERVAL (SV_NAME_F1 (cos), 0, 0xffff0000, 10000)
81 TEST_INTERVAL (SV_NAME_F1 (cos), 0x1p-4, 0x1p4, 500000)
82 CLOSE_SVE_ATTR
83